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Seminários do IMPA

Geometria Diferencial

Título
Holomorphicity of real Kähler submanifolds
Expositor
Alcides de Carvalho Júnior

IMPA
Data
Terça-feira, 1 de outubro de 2019, 15:30
Local
Sala 236
Resumo

I will talk on a recent joint paper with S. Chion and M. Dajczer.


Let $f\colon M^{2n}\to\mathbb{R}^{2n+p}$ denote an isometric immersion of a Kähler manifold of complex dimension $n\geq 2$ into Euclidean space with codimension $p$. If $2p\leq 2n-1$, we show that generic rank conditions on the second fundamental form of the submanifold imply that $f$ has to be a minimal submanifold. In fact, for codimension $p\leq 11$ we prove that $f$ must be holomorphic with respect to some complex structure in the ambient space.